A6.5 - Typical injury accident rates and prediction models

Introduction

The typical accident rates and prediction models of reported injury accidents presented in this section are the result of studies carried out for Transit NZ and Land Transport NZ. Accident prediction models and exposure-based accident prediction equations differ in how they relate accidents to traffic volumes.

The exposure-based accident prediction equations in this section assume that the number of accidents at a site is directly proportional to traffic volume. That is, if the traffic volume doubles then the number of accidents will also double (if everything else remains the same).

However, for the accident prediction models the number of accidents per vehicle varies depending on the traffic volume. Therefore a doubling in traffic volume will not result in an accident rate that is double - in such cases the predicted accident rate can be significantly different from double the number of accidents.

Definition of exposure

Exposure to the risk of having an accident is defined as follows:

(a) For mid-blocks, exposure is the number of vehicle-kilometres of travel on the mid-block, measured in hundred million vehicle-kilometres per year, ie

where L is the section length in kilometres, and AADT is the annual average
daily traffic.

(b) For sites, or parts of sites, other than mid-blocks, exposure is the number of vehicles travelling through, measured in hundred million vehicles per year, ie

Types of terrain

In rural areas, the values for model co-efficients are based on different terrain types, defined as follows:

Definition of movement category

There are movement categories which are groupings of the two letter movement codes used in CAS to categorise accidents. Figure A6.1 shows the CAS movement codes.

Figure A6.1 CAS movement codes (version 2.4 February 2005)

General and conflicting flow models

General models are suitable for most mid-block or intersection types indicated. Where a breakdown of accidents by accident type or road user type is required; or, in the case of intersections, where the proportion of turning vehicles is high compared to through vehicles, then conflicting flow models should be used.

Available models and equations

This section contains general and conflicting flow accident prediction models and exposure-based accident prediction equations for:

Application of models and equations

All accident prediction models and exposure-based accident prediction equations calculate total injury and fatal accidents per year. The models and equations are valid within the flow ranges provided. Analysts should exercise caution when using the models and equations outside these ranges.

The accident prediction models and exposure-based accident prediction equations in this section have been developed for the most common types of site in each category. For example, traffic signal models were developed for two and three phase signals, and are therefore not as accurate for signals with four or more phases, or where there are a lot of phase changes during set periods of the day.

The more unusual a site is from the typical site type, the less appropriate the general models and equations will be for predicting the typical accident rate. In most cases where there is a feature of a site, such as the site's layout, that has a significant effect on the accident rate, the models and equations in this section are not likely to be appropriate.

Models and equations from other sources

Analysts are permitted to use accident prediction models and exposure-based accident prediction equations from other sources, as long as the robustness of these other sources can be demonstrated. These sources need to be referenced (eg, papers, research reports or unpublished material), along with information on sample size, modelling technique and goodness-of-fit statistics.

For intersection and mid-block accident prediction models, analysts are referred to the appropriate research report on accident prediction models. The accident prediction models in these reports are useful for determining the effects of varying traffic demands on particular movements at intersections, mode split and site specific features.

(1)General cross and T urban intersection 50-70 km/h

The 'general' model is suitable for most urban cross and T intersection types and uses two-way link volumes where the posted speed limit is 50-70 km/h. Where a breakdown by accident type and road user type is required, or where the proportion of turning vehicles is high compared to through vehicles, then the appropriate conflicting flow models should be used.

For urban intersections on the primary road network (excluding roundabouts), the typical accident rate (reported injury accidents per year) is calculated using:

A_T = b₀ × Q_major^b1 × Q_minor/side^b2

where:

Q_major the highest two-way link volume (AADT) for cross-roads and the primary road volume for T-junctions

Q_minor/sidethe lowest of the daily two-way link volumes (AADT) for cross-roads and the side road flow for T-junctions

b₀, b₁ and b₂ are given in table A6.2(a).

Table A6.2(b) shows the range of flows over which the accident prediction models should be applied. The k values are for use in the weighted accident procedure.

Caution

Caution should be exercised when using the prediction models for intersections where opposing approach flows (on Q_major or Q_minor) differ by more than 25 percent. In such cases, conflicting flow models should be used.

Table A6.2(a) Urban intersection injury accident prediction model parameters (2006)

Table A6.2(b) Urban intersection injury accident flow ranges and k values

(2) General urban roundabouts, 50-70 km/h

Often roundabouts do not have the roads with the highest or lowest volumes on opposing arms, or if they have three arms these are seldom in a 'T'. Therefore, accidents are calculated for each arm of the roundabout, and the total obtained by adding these together. The typical accident rate (reported injury accidents per approach per year) is calculated using the model:

A_T = b₀ × Q_approach^b1

where:

Q_approach the two-way link volume (AADT) on the approach being examined.

b₀, and b₁ are given in table A6.3(a).

This model can be applied for roundabouts with three, four or five approaches. Table A6.3(b) shows the range of flows over which the accident prediction model should be applied. The k values are for use in the weighted accident procedure.

Table A6.3(a) Urban roundabout injury accident prediction model parameters (per approach - 2006)

Table A6.3(b) Urban roundabout injury accident prediction model flow ranges (per approach) and k values

(3)Conflict - urban signalised crossroads, < 80 km/h

The conflicting flow models for signalised crossroads are suitable for situations where a breakdown of accidents by accident and road user type is required, or where the proportion of turning vehicles is high compared to through vehicles.

For urban (speed limit < 80 km/h) signalised crossroads on the primary road network the typical accident rates can be calculated for the six accident types (13, 19) in table A6.4(a).

Table A6.4(a) Urban signalised crossroad accident prediction models types

The number of reported injury accidents per year for each accident type on each approach can be calculated using the models in table A6.4(b). These models calculate the number of accidents per approach and therefore must be used for each approach to the intersection.

Table A6.4(b) Urban signalised crossroad accident prediction models (per approach - 2006)

(4)Conflict - urban roundabouts, < 80 km/h

The conflicting flow models for roundabouts are suitable for situations where a breakdown of accidents by accident and road user type is required, such as roundabouts with high proportions of cyclists.

For urban (speed limit < 80 km/h) roundabouts on the primary road network the typical accident rates can be calculated for the seven accident types (15) in table A6.5(a).

Table A6.5(a) Urban roundabout accident prediction models types

(4)Conflict - urban roundabouts, < 80 km/h

The number of reported injury accidents per year for each accident type on each approach can be calculated using the models in Table A6.5 (b). These models calculate the number of accidents per approach and therefore must be applied at all approaches to the roundabout.

Table A6.5(b) Urban roundabout accident prediction models (per approach - 2006)

(5)General urban mid-blocks, 50-70 km/h

The 'general' models are suitable for most urban mid-blocks (2 to 4 lane road) types in posted speed limit areas of 50-70 km/h. The typical accident rate (reported injury accidents per year) is dependent on roadside development, and for arterials, the presence of a median. separate pedestrian and cyclist models are available. All reported injury accidents are calculated using the model:

A_T = b₀ × Q_T^b1 × L

where: Q_T is the daily two-way traffic volume (AADT)
L is the length of the mid-block site

b₀ and b₁ are given in table A6.6(a). Use the commercial classification when the majority of roadside development is either commercial or industrial, while 'other' is for residential and all other types.

Table A6.6(b) shows the range of flows and speed limits over which the accident prediction models should be applied. The arterial models can be used for 50 and 60 km/h speed limit areas. The collector and local street models are applicable for 50 km/h speed limit areas only. The k values are for the weighted accident procedure.

Arterials with ≥6 lanes

There is currently no information available for six or more lane arterials. The arterial model can be used as in the weighted accident procedure (Method C) with a reliability factor, a_M, of 1.5. Six-lane roads are likely to have a greater proportion of weaving related accidents, particularly where intersections are closely spaced.

Effect of medians

A reduction of 15 percent in the accident prediction for arterial and collector mid-blocks should be applied for flush medians. A reduction of 25 percent in the accident prediction for arterial mid-blocks should be applied for raised medians. Note that raised medians can migrate accidents to adjacent intersections.

Table A6.6(a) Urban mid-block injury accident prediction model parameters (2006)

Table A6.6(b) Urban mid-block injury accident prediction model flow ranges and k values

(6)Conflict - urban mid-block - pedestrian and cyclist facilities

The pedestrian or cyclist models are required when using accident rate analysis to assess a new or improved pedestrian or cyclist facility. These rates are for urban (speed limit < 80 km/h) areas and do not include any pedestrian or cyclist accidents that occur at side roads. However, driveway accidents are included. The typical accident rates can be calculated for the accident types in table A6.7(a).

The number of reported injury accidents per year for each accident type is calculated using the models in table A6.7(b).

Table A6.7(a) Urban mid-block pedestrian and cycle accident prediction model types

Table A6.7(b) Urban mid-block pedestrian and cycle accident prediction models (2006)

(7) General high speed cross and T intersections, ≥80 km/h

The 'general' model is suitable for most high speed cross and T intersections and use two-way link volumes. Where a breakdown of accidents by accident and road user type is required, or where the proportion of turning vehicles is high compared to through vehicles then conflicting flow models should be used.

For high speed cross and T intersections, the typical accident rate (reported injury accidents per year) is calculated using the model:

A_T = b₀ × Q_major^b1 × Q_minor/side^b2

where:

Q_major the highest two-way link volume (AADT) for cross-roads and the primary road volume for T-junctions

Q_minor/side the lowest of the daily two-way link volumes (AADT) for cross-roads and the side road flow for T-junctions.

b₀, b₁ and b₂ are given in table A6.8(a).

Table A6.8(b) shows the range of flows over which the accident prediction models should be applied. The k values are for use in the weighted accident procedure.

Caution

Caution should be exercised when using the prediction models for intersections where opposing approach flows (on Q_major or Q_minor) differ by more than 25 percent. In such cases, conflicting flow models should be used.

Table A6.8(a) High speed intersection injury accident prediction model parameters (2006)

Table A6.8(b) High speed intersection injury accident flow ranges and k values

(8)Conflict - high speed roundabout

Often roundabouts do not have the roads with the highest or lowest volumes on opposing arms, or if they have three arms these are seldom in a 'T'. Therefore, accidents are calculated for each arm of the roundabout, and the total obtained by adding these together. The typical accident rate (reported injury accidents per approach per year) is calculated using the model:

A_T = b₀ × Q_approach^b1

where:

Q_approach the two-way link volume (AADT) on the approach being examined.

b₀, and b₁ are given in table A6.9(a).

This model can be applied for roundabouts with three or four approaches. Table A6.9(b) shows the range of flows over which the accident prediction model should be applied. The k values are for use in the weighted accident procedure.

Table A6.9(a) High speed roundabout injury accident prediction model parameters (per approach - 2006)

Table A6.9(b) High speed roundabout injury accident prediction model flow ranges (per approach)

(9)Conflict - high speed priority crossroads, > 70 km/h

The conflicting flow models for priority crossroads in high-speed areas are suitable for situations where a breakdown of accidents by accident type is required, or where the proportion of turning vehicles is high compared to through vehicles.

For high speed (speed limit > 70 km/h) priority crossroads on two-lane, two way roads the typical accident rates can be calculated for the five accident types in table A6.10(a).

Table A6.10(a) High speed priority crossroad accident prediction models types

The number of reported injury accidents per year for each accident type is calculated table A6.10(b). These models calculate the number of accidents per approach. However, unlike urban roundabout and signalised crossroad models, each model is only applied to two approaches only (not all four). These approaches are specified as either 'major road' or 'minor road' with the minor road being the road with stop or give way control.

Table A6.10(b) High speed priority crossroad accident prediction models (per approach -2006)

(10)Conflict - high speed priority T-junctions, > 70 km/h

The conflicting flow models for priority T-junctions in high-speed areas are suitable for situations where a breakdown of accidents by accident type is required, where one turning movement from the side road is greater than the other, or where the intersection has a visibility deficiency.

For high speed (speed limit > 70 km/h) priority T-junctions on two lane, two way roads the typical accident rates can be calculated for the five accident types in table A6.11(a).

Table A6.11(a) High speed priority T-junctions accident prediction models types

The typical accident rate (number of reported injury accidents) per year for each accident type is calculated using table A6.11(b). Unlike models for other intersections, these models are each for a specific approach.

Table A6.11(b) High speed priority T-junction accident prediction models (2006)

(11) Rural two-lane roads, ≥ 80 km/h

For two-lane rural roads in 80 and 100 km/h speed limit areas, the typical accident rate (reported injury accidents per year) is calculated using the exposure-based equation:

A_T = (b₀ × S_adj) × X

where:

S_adj is the cross section adjustment factor for seal widths

X is the exposure in 100 million vehicle kilometres per year.

Coefficient b₀ is provided in table A6.12(a). The coefficient b₀ is applicable to a given mean seal width. S_adj  is found in table A6.13, and varies according to traffic flow, seal shoulder width and lane width.

The terrain type for b₀ can be selected by analysing the route gradient data. The gradient ranges should generally be maintained throughout the road section. Portions of road that are less steep can occur in mountainous sections for short lengths. Provided that the lower gradient length is followed by another mountainous gradient, then the entire section can be classified as mountainous.

Table A6.12(b) shows the k values per kilometre that should be used in the weighted accident procedure.

Table A6.12(a) Rural mid-block equation coefficients (b0) (2006)

Table A6.12(b) Rural mid-block k values per km

Applying the cross-section adjustment factors

Table A6.13 provides adjustment factors for two lane rural accident rates for various combinations of seal widths that differ from the mean seal widths in table A6.12(a).

First, the overall seal width, shoulder width and lane width is determined. Then, look up S_adj that corresponds to the traffic volume, shoulder width and lane width in table A6.13. Adjust b₀ by multiplying with the adjustment factor and use this value to calculate the typical accident rate.

In the case of shoulder widening, different adjustment factors must be used for the do minimum and option.

Effect of crash barriers

In mountainous and rolling terrain the typical accident rates can be reduced by 25 percent when crash barriers are installed to protect errant vehicles from drop-off areas and other obstacles in the roadside clear zone.

3-4 lane rural roads

For three and four lane rural roads refer to appendix A6.5 on passing lanes.

Worked example

An example of the use of the cross-section adjustment factors in table A6.13 is provided in appendix A6.8.

Table A6.13 Cross-section adjustment factors (S_adj)

(12) Rural two-lane roads: heavy vehicles, ≥ 80 km/h

For freight transport service proposals, where the road network affected by the proposal are primarily two-lane rural roads in 80 and 100 km/h rural areas, accident rate equations for accidents involving heavy vehicles can be used to estimate the change in freight related accidents.

The typical heavy vehicle accident rate (reported injury accidents involving heavy vehicles per year) is calculated using the exposure-based equation:

A_H = b₀ X

where: X is the exposure in 100 million heavy vehicle kilometres per year.

Coefficient b₀ is provided in table A6.14.

Table A6.14 Rural mid-block equation coefficients (b₀) for heavy vehicles (2006)

(13) Motorways and 4-lane divided rural roads

The typical accident rate (reported injury accidents per year) for motorways and four-lane divided rural roads is for a one directional link only and is dependent on the one-way traffic volume.

Motorways

The typical accident rate is calculated using the model:

A_T = b₀ × Q_O^b1 × L

where: Q_O is the daily one-way traffic volume (AADT) on the link, and
L is the length of the motorway link.

b₀ and b₁ are given in table A6.15(a).

Table A6.15(b) shows the range of one-way flows over which the accident prediction models should be applied. The k values are for use in the weighted accident procedure.

4-lane divided rural roads

For four-lane divided rural roads, the same motorway accident prediction model is used. The b₀ coefficient from this model has been increased by 20% to take into account the presence of pedestrians, cyclists and limited access provisions of rural roads compared to motorways.

Table A6.15(a) Motorways and 4-lane divided rural roads mid-block injury accident prediction model parameters

Table A6.15(b) Motorways and 4-lane divided rural roads mid-block injury accident prediction model flow ranges and k values

(14) Conflict - rural isolated curves, ≥ 80 km/h

Figure A6.2 and the equation below provide typical accident rates for reported injury loss of control and head-on accidents on rural curves, adjusted for the general trends in accidents. They should be used only for an isolated curve that is replaced with a single curve of a higher design speed.

The data for typical injury accident rates has been based on sealed rural state highways. An underlying assumption is that the road section under consideration is not affected by ice or other adverse factors such as poor visual conditions.

The typical accident rate (reported injury accidents per year, by CAS movement categories B, C and D) for an isolated rural curve is calculated using the equation:

A_T = b₀ X e^{(b1 S)}

where: b₀ = 4.1

b₁ = 2.0

X is the exposure in 100 million vehicles (in one direction) passing

through the curve, and

S = 1- design speed of curve / approach speed to curve

A_T must be calculated for both directions, and S is likely to vary between the two directions. If the design speed is approximately equal to the approach speed then the equation reduces to:

A_T = b₀ X

A k value of 1.1 is used in the weighted accident procedure.

Assumptions

The following assumptions apply when using the equation or figure A6.2:

1. for figure A6.2 the rate is in terms of injury accidents per 100 million vehicles, and for the equation the rate is in injury accidents per year through the curve
2. the design speed of the curve should be determined from a standard design reference
3. the approach speed to the curve is the estimated 85^th percentile speed at a point prior to slowing for the curve (for longer tangents this would approximate to the speed environment).

Figure A6.2 Injury accidents per 100 million vehicles for rural curves in 100 km/h speed

limit areas for type B, C and D accidents (2006)

(15) Rural passing lanes accident adjustment factor

The construction of passing lanes on rural roads (posted speed limit ≥80 km/h) has the effect of reducing the typical accident rate calculated using the rural two lane roads model for both the road section and for the road downstream of the passing lane.

Where a passing lane is constructed in one direction only, for the road section alongside the passing lane, the reduction in the typical accident rate is 25% for both directions of travel. The reduction in the typical accident rate decreases linearly to zero from the end of the passing lane to either the location where vehicle platooning returns to normal (generally 5 to 10 km downstream), or where another passing lane begins.

Where passing lanes are constructed in both directions at the same location, no further accident reduction along the length of the passing lane is permitted. Downstream benefits can be calculated for either side of the section of passing lanes.

There are currently no conclusive research findings available on the upstream benefits of installing passing lanes. At this stage, no reduction in the b₀ coefficient is permitted for benefits upstream.

If a passing lane is being constructed to address a specific accident type, an appropriate accident reduction factor may be found in appendix A6.6.

(16) Single lane rural bridges, ≥ 80 km/h

The typical accident rate (reported injury accidents per year) of a single lane bridge on a rural road (≥80 km/h) is determined by the equation:

A_T = b₀ X

where: X is the exposure in 100 million vehicles crossing the bridge per year

b₀ = 10.1 (Q_T)^0.3 (2006 analysis year)

Q_T being the two-way daily traffic volume (AADT).

This equation does not take into account low design speed approach curves (65 km/h advisory speed or less), traffic signal control or adjoining intersections within 200 m of the bridge.

(17) Two lane rural bridges, ≥ 80 km/h

The typical accident rate (reported injury accidents per year) of a two-lane bridge on a rural road (≥80 km/h) is determined by the equation:

A_T = b₀ X

where: X is the exposure in 100 million vehicles crossing the bridge per year
b₀ = 0.96 × c × (0.5 − 0.25 RW + 0.025 RW²) (2006 analysis year)

with RW being the difference between the seal width across the bridge and the total sealed lane width in metres (both directions) on the bridge approaches (normally 7 m on State highways). A narrow bridge seal width leads to a negative value for RW. The limits of RW are governed by the limiting width for single lane operation (for the maximum negative value of RW) and 2.5 m (maximum positive value of RW).

The value of c is given by the formula:

c = e^{(3.5 − Q}_T ^{/ 7,500)}

where: Q_T is the two-way daily traffic volume (AADT).

This model does not take into account low design speed approach curves (65 km/h advisory speed or less) or adjacent intersections within 200 m of the bridge.

In the weighted accident procedure, use the k-values provided in table A6.16.

Table A6.16 Rural bridge k values

(18) Urban and rural railway crossings

For urban and rural railway crossings, the typical accident rate (reported injury hit train and rear-end accidents per year) is calculated using the model:

A_T = b₀ × T^b1 × Q_T^b2

where: T is the number of trains per day

Q_T is the daily two-way traffic volume (AADT)

b₀, b₁ and b₂ are given in table A6.17(a)

Table A6.17(b) shows the range of traffic volumes and trains over which the accident prediction models should be applied.

The k values are for use in the weighted accident procedure.

A large number of railway crossings are located in close proximity to low design speed curves. Low design speed approach curves are often caused by the route having to deviate sharply when crossing the railway line. In such circumstances separate predictions of the typical accident rates on these approach curves need to be made using the model for rural isolated curves (≥80 km/h).

Table A6.17(a) Railway crossing accident prediction model parameters (2006)

Table A6.17(b) Railway crossing accident prediction model traffic volumes ranges and k values